1. True/False Prove if true and give a counter example if false. 1. True/False Prove if true...

1. True/False Prove if true and give a counter example if false.

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1. True/False Prove if true and give a counter example if false. In this problem, we take | -| to be the usual Euclidean 2-norm. (a) Suppose that all the eigenvalues of the matrix A have negative real part. Then solution of the differential equation r' = Ar satisfies, every |r(t)| < |r(s)|, if t > s. 1. True/False Prove if true and give a counter example if false. In this problem, we take | -| to be the usual Euclidean 2-norm. (a) Suppose that all the eigenvalues of the matrix A have negative real part. Then solution of the differential equation r' = Ar satisfies, every |r(t)| < |r(s)|, if t > s.